unit 9 – factoring polynomials topic: greatest common factors
TRANSCRIPT
Unit 9 – Factoring Polynomials
Topic: Greatest Common Factors
Vocabulary
• Factor Whole number divisors of another whole number. Ex. 3 is a factor of 27 Variable divisors of another variable. Ex. x2 is a factor of x5
• Common factors Factors shared by two or more monomials. Ex. 3 is a common factor of 9 and 27
• Greatest Common Factor (GCF) Largest common factor of two or more monomials. Ex. 9 is the GCF of 9 & 27
Prime Factorization
• Prime number factors of a whole number.Prime factors can be found using a factor tree.
602 30Prime number
2 153 5
5322 5322
Finding GCF of numbers – Listing factors
• List factors of each number and identify the GCF.
• Example: Find the GCF of 18 and 27.Factors of 18: 1, 2, 3, 6, 9, 18Factors of 27: 1, 3, 9, 27GCF = 9
Finding GCF of numbers – Using Factor Trees
• Find the prime factors of each number. The GCF will be the product of common primes.
• Example: Find the GCF of 18 and 27.Prime factorization of 18: 2 x 3 x 3Prime factorization of 27: 3 x 3 x 3Common primes: 3 x 3GCF = 9
Finding GCF of variables
• GCF will include a common variable base & the lowest exponent of given terms.
• Example: Find the GCF of x3, x5y, & x4y2
Common variable base: x (1st term doesn’t have a y in it)
Lowest exponent of x: 3GCF of x3, x5y, & x4y2= x3
Finding GCF of monomials
• Must find GCF of coefficients AND variable(s).
• Example: Find the GCF of 3x3 and 6x2
GCF of 3 & 6: 3
GCF of x3 and x2: x2
GCF of 3x3 & 6x2= 3x2
Factoring polynomials by GCF
• Rewriting polynomials as products of monomials & polynomials that cannot be factored further.
• Find GCF of the given terms, then factor (divide) it out.Example: Factor the polynomialGCF = 5y; divide each term by 5y to find
remainders.
• NOTE: GCF MUST appear in final answer (Think of factoring as “un-distributing”).
yyy 52010 23
)142(5 2 yyy
Factoring out a common binomial
• Two monomials that are multiplied by the same binomial.
• The binomial can be factored out, leaving the two monomials together to form another binomial.Example: Factor (x – 2) factors out, leaving 4x & 5 to form a
binomial.
)2(5)2(4 xxx
)54)(2( xx
Factoring by grouping
• Grouping terms of a polynomial by similar GCFs to find a common binomial.Example: Factor 1592012 23 xxx
)34(5)34(3 2 xxx
)1520()912( 23 xxx
Rewrite the polynomial in standard form, then group the first 2 terms & the last 2 terms.
Factor a GCF out of each group (this should give you a common binomial).
)53)(34( 2 xxFactor out the common binomial.
Journal EntryTitle: GCF 3-2-1• Identify 3 things you already knew from the material
in the PowerPoint.
• Identify 2 new things you learned.
• Identify 1 question you still have.
Homework
• Textbook Section 8-1 (p. 527): 16-30 even
• Textbook Section 8-2 (p. 535): 28-36 even, 44-54 even
• DUE 3/16